The linear span of isomorphism classes of posets, P, has a Newtonian coalgebra structure. We observe that the ab-index is a Newtonian coalgebra map from the vector space P to the algebra of… (More)

We generalize the notion of the rank-generating function of a graded poset. Namely, by enumerating different chains in a poset, we can assign a quasi-symmetric function to the poset. This map is a… (More)

We consider juggling patterns where the juggler can only catch and throw one ball at a time, and patterns where the juggler can handle many balls at the same time. Using a crossing statistic, we… (More)

We obtain an explicit method to compute the cd-index of the lattice of regions of an oriented matroid from the ab-index of the corresponding lattice of flats. Since the cd-index of the lattice of… (More)

We prove that thecd-index of a convex polytope satisfies a strong monotonicity property with respect to the cd-indices of any face and its link. As a consequence, we prove for d-dimensional polytopes… (More)

We introduce a large self-dual class of simplicial complexes about which we show that each complex in it is contractible or homotopy equivalent to a sphere. Examples of complexes in this class… (More)

We present a probabilistic approach to studying the descent statistic based upon a two-variable probability density. This density is log concave and, in fact, satisfies a higher order concavity… (More)

We generalize the notion of a binomial poset to a larger class of posets, which we call Sheffer posets. There are two interesting subspaces of the incidence algebra of such a poset. These spaces… (More)

In this paper we generalize the cd -index of the cubical lattice to an r cd -index , which we denote by Õ ( r ) . The coef ficients of Õ ( r ) enumerate augmented Andre ́ r -signed permutations , a… (More)